The Syrian extremist militia Jabhat al-Nusra is a branch of al Qaeda’s coalition in Iraq and has been all along, the umbrella group Islamic State of Iraq acknowledged Tuesday — a move that shows the blossoming self-confidence of salafist jihadis about their role in the revolution raging in Syria.

The news came as Secretary of State John Kerry said the U.S. was considering increasing its aid to the Syrian rebels in ways which will have “an impact on President Assad’s calculations about where the battlefield is going.”

“It’s now time to declare in front of the people of the Levant and world that Jabhat al Nusrah is but an extension of the Islamic State of Iraq and part of it,” said an audio message from the emir of the Iraqi coalition group, Abu Bakr al-Ḥussayni al-Qurayshi al-Baghdadi.

The statement was translated by the Site Intelligence Group, a firm which monitors extremist messaging. It was confirmed by postings on jihadi message boards and web forums.

“This is major news,” declared Peter Bergen, a leading al Qaeda scholar and a senior fellow at the New America Foundation, a centrist think tank.

“It means al Qaeda is confident enough about its position in Syria to go public,” said Aaron Zelin, editor of the blog Jihadology. “Their perception is correct because their position is strong” in the ranks of Syria’s fractious and ill-disciplined rebels, he added.

In the audio statement, al-Baghdadi said the original members of Jabhat al-Nusra, also known as the al-Nusra Front, were dispatched from Iraq by his group, the Islamic State of Iraq, a coalition of al Qaeda and other extremist groups and militias that came together during their bloody insurgency against the U.S. occupation.

“We laid for them plans, and drew up for them the policy of work, and gave them what financial support we could every month, and supplied them with men who had known the battlefields of jihad, from the emigrants and the natives,” al-Baghdadi said.

The leader of Jabhat al-Nasra, Abu Muhammad al-Julani, is one of al-Baghdadi’s subordinates, that he “deputized” to establish a branch of al Qaeda in Syria, the statement said.

The new merged organization will be called the Islamic State of Iraq and al-Sham (the Levant), he said, according to the Site translation.

Mr. Bergen said the move was an over-reach that both groups would have cause to regret, but especially the Syrians. “It’s a dumb idea,” he said, “I don’t see the strategic advantage [for al-Nusra] in linking themselves to al Qaeda.”

Even slain al Qaeda leader Osama bin Laden had in the last few years before his May 2011 death begun recommending to the network’s affiliates and supporters that they not take al Qaeda’s name, Mr. Bergen noted, citing documents declassified from the trove recovered by U.S. special forces at bin Laden’s hideout.

Mr. Zelin, a scholar at the Washington Institute for Near East Politics said that the strength of al-Nusra in Syria sprang from involvement in local governance in rebel-controlled areas of the country. Fighters from the internationally-backed rebel coalition, the Free Syrian Army, notoriously engaged in “looting and extorting” the local people through high prices and high taxes in areas they controlled, he said. By contrast, al-Nusra fighters were disciplined and supplied bread and fuel at below market prices.

In the Syrian areas they control, said Mr. Zelin, al-Nusra had banned alcohol, enforced the veil and introduced lashing as a punishment for fraternization between men and women. But the group so far appeared to be avoiding the more extreme manifestations of their austere version of islamic law, like public beheadings and stonings, or banning music or women leaving their houses without their husband or a male relative.

Mr. Zelin said a backlash against al-Nusra’s social agenda “could be a long or medium terms problem, but is not an issue in the short term.”

The news from Syria came as the secretary of state, visiting the middle east, hinted that the United States might be about to step up its aid to Syrian rebels, perhaps expanding the range of support it provides. Current only non-lethal aid is provided by the United States, although the New York Times among others has reported that U.S. intelligence is working closely with Arab security agencies that are arming certain elements of the loose rebel alliance.

“Yes, I will be meeting with the Syrian opposition in London, and, yes, we will be discussing various means of having an impact on President Assad’s calculations about where the battlefield is going,” Mr. Kerry told reporters Tuesday.

He said he would “leave it to the White House … to make any announcements with respect to any stepped-up efforts.”

“I’m not sure what the schedule is,” he added, hinting at a future policy adjustment, “but … we’ll see what is forthcoming on that in the days ahead.”